Invalidity of Preissmann Scheme for Transcritical Flow
Publication: Journal of Hydraulic Engineering
Volume 123, Issue 7
Abstract
The Preissmann scheme, often referred to as the four-point scheme, is a bidiagonal implicit finite-difference method for solution of the de St. Venant equations. It is unconditionally stable and extremely robust, and thus is one of the most widely used methods in free-surface one-dimensional subcritical numerical modeling. The purpose of this technical note is to discuss the limitations of Preissmann scheme when applied to transcritical flow. In particular, the analysis presented shows that the Preissmann scheme cannot be used to simulate transcritical flow using the through (shock capturing) method.
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References
1.
Abbott, M. B. (1979). Computational hydraulics: elements of the theory of free surface flows. Pitman Publishing, Ltd., London, U.K.
2.
Abbot, M. B., Havno, K., and Lindberg, S.(1991). “The fourth generation of numerical modeling in hydraulics.”J. Hydr. Res., 29(5), 581–600.
3.
Cunge, J. A., Holly, F. M. Jr., and Verwey, A. (1980). Practical aspects of computational river hydraulics. Pittman Publishing Ltd., London, U.K.
4.
De St. Venant, B.(1871). “Theorie du mouvement non-permanent des eaux avec application aux crues des riveres et a l'introduction des Marees dans leur lit.”Academie de Sci. Comptes Redus, 73(99), 148–154.
5.
Dooge, J. C. I., and Napiorkowski, J. J.(1987). “The effect of the downstream boundary conditions in the linearized St. Venant equations.”Quarterly J. Mech. and Appl. Math., 40(2), 245–256.
6.
Fennema, R. J., and Chaudhry, M. H.(1986). “Explicit numerical schemes for unsteady free-surface flows with shocks.”Water Resour. Res., 22(13), 1923–1930.
7.
Havno, K., and Brorsen, M. (1985). “Generalized mathematical modeling system for flood analysis and flood control design.”Proc., Int. Conf. on Hydr. of Floods and Flood Control, British Hydrodynamics Research Assoc. (BHRA), Stevenage, U.K.
8.
Jameson A., Schmidt, W., and Turkel, E. (1981). “Numerical simulation of the Euler equations by finite volume methods using Runge Kutta time stepping schemes.”Proc., 5th Computational Fluid Dyn. Conf., American Institute of Aeronautics and Astronautics, Washington, D.C.
9.
Kutija, V.(1993). “On the numerical modeling of supercritical flow.”J. Hydr. Res., 31(6), 841–858.
10.
Meselhe, E. A. (1994). “Numerical simulation of transcritical flow in open channels,” PhD thesis, The University of Iowa, Iowa City, Iowa.
11.
Preissmann, A. (1961). “Propagation des Intumescences dans les canaux et Rivieres.”1st Congr. des l'Assoc. Francaise de Calcul, Association Francaise de Calcul, Grenoble, France, 433–442.
12.
Pulliam, T. H.(1986). “Artificial dissipation models for the Euler equations.”AIAA J., 24(12), 1931–1940.
13.
Samuels, P. G., and Skeels, C. P.(1990). “Stability limits for Preissmann's scheme.”J. Hydr. Engrg., ASCE, 166(8), 997–1012.
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Copyright © 1997 American Society of Civil Engineers.
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Published online: Jul 1, 1997
Published in print: Jul 1997
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